The ancient Greeks were fond of dividing into sixties; this division still con tinues in our scales for angles and for time; and it is worthy of remark, that if we divide the whole circumference of the earth into 60 parts, each of these into 60, and again each into 60, we arrive at a distance of 607.5 English feet. Now, the. length of the ancient Greek stadium or furlong is stated to be 606i ft. by some writers; and if deduced from measures of the Roman mile, is between 605 and 613 ft.; so that if we desire a cosmo politan standard, we can hardly do better titan go back to the ancient Greek stadium or the Chinese /i, corrected to suit the more accurate determination of modern times: this would bring us to the geographical foot, one-hundredth part of a second of the earth's meridian.
The standard of weight is readily connected with the standard of measure. Some substance which can be easily obtained pure is chosen, and a definite bulk of it is weighed. Distilled water is universally selected for this purpose; and in the British system the weight of one cubic inch of pure water is declared to be 252.458 grains when it is at the temperature of 62° Fahr.
It has long been known that water does not continue to contract as it is cooled; the contraction becomes less and less as the temperature approaches to 41° or 39° Fahr. ; and the water, when cooled more, begins to expand, and continues to grow more bulky until it be on the point of freezing. On this account it has been proposed, and without any doubt it would be the best plan, to take water when at its greatest density as the stand ard for comparison, because then an error of a degree in temperature will produce no perceptible error in the weight.
The operation of verifying the standard of measure by it with the size of the earth is necessarily an expensive and a complicated one, only to comparing attempted under the auspices of a wealthy government, or with the concurrence of several nations; and it is desirable to find out something more local and more easily obtained wherewith to compare our measures. The length of the pendulum (q.v.) has been proposed ; and, on account of a very simple and beautiful property of pendulums, the comparison can be readily made. If we imagine an excessively minute heavy body to be suspended by a thread so fine that the weight of the thread may be neglected, the compound so formed is called a simple pendulum; and the question becomes, what must be the length of such a pendulum in order that it may vibrate from side to side in, say, one second timc? Now, it is clear that we cannot obtain this length by direct experiment, since we cannot construct such a pendulum. M. Biot tried to approximate to it byls 'ng a small m, a ball of platinum hung by a very fine wire. However, it is known that if heavy rigid mass be suspended by a knife-edge, and if its vibrations be made in the f e same with those of a simple pendulum, then if we place another knife-edge at a distance from the first equal to the length of the pendulum and reverse the ends, the compound pendulum will again vibrate in the same time as before. Hence we have a very simple method of
e comparison. Having constructed a strong bar with two knife dges at a known distance from each other, say at the distance of a yard, let us then, by many trials, filings, and s scrapings, so adjust it as that the times of vibration shall be ake for the two knife-edges, and, finally, let us count how many vibrations such a pendulum makes per day, and then we shall have a means of verifying our measure.
The act of parliament which fixes our present weights and measures enacts that the length of a pendulum vibratinn. in one second of mean solar time is 39.13929 in.; now the lengths of pendulums are proportional, not to the times in which they vibrate, but to the squares of those times; and so if we know the length of one pendulum, and the number of vibrations it makes per day, we can calculate what ought to be the length of another to vibrate a given number of times. A convertible pendulum having the dis tance between its knife-edges exactly 36 in. ought to make 90088.42 vibrations per day.
When only a degree of accuracy sufficient for commercial and ordinary purposes is aimed at, the above process is by no means difficult; but when extreme precision is wanted, the operation is attended with many and very great difficulties; it involves considerations which would hardly have been expected. In the first place, our experi ments are made in air, and the buoyancy of the air lessans the actual weight of the pendulum; that buoyancy has to be allowed for, and therefore it is declared that the above length is that of a pendulum vibrating in a vacuum. Next, since the earth has a diurnal motion on its axis, every substance placed on it has a centrifugal tendency which goes to modify what otherwise would have been its gravitation; this centrifugal tendency produces the earth's oblateness, and causes a variation in the gravi tation from one latitude to another. A stone is actually heavier in Edinburgh than it is in London. This change in gravitation cannot be measured by a balance, because the weights at each end of the balance are changed alike; but is seen at once in the going of a clock; for a pendulum regulated to go truly in London is found to go too fast when taken to a higher latitude, and to lose time when carried nearer to the equator. Hence, the enactment that the pendulum must be swung in the latitude of London. And again, the attraction which the earth exerts upon bodies placed near it diminishes with their distances, being inversely as the squares of the distances; hence, a clock carried from the bottom to the top of a bill loses time perceptibly, and so it is necessary to have the additional enactment that the pendulum be swung at the level of the sea.